• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.4C
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• pp.379-388
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• 2007

In this paper, we propose an adaptive turbo decoding algorithm for high order modulation scheme combined with originally design for a standard rate-1/2 turbo decoder for B/QPSK modulation. A transformation applied to the incoming I-channel and Q-channel symbols allows the use of an off-the-shelf B/QPSK turbo decoder without any modifications. Adaptive turbo decoder process the received symbols recursively to improve the performance. As the number of iterations increase, the execution time and power consumption also increase as well. The source of the latency and power consumption reduction is from the combination of the radix-4, dual-path processing, parallel decoding, and early-stop algorithms. We implemented the proposed scheme on a field-programmable gate array (FPGA) and compared its decoding speed with that of a conventional decoder. From the result of implementation, we confirm that the decoding speed of proposed adaptive decoding is faster than conventional scheme by 6.4 times.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.12C
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• pp.1739-1747
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• 2004

In this paper, an efficient radix-4 systolic VLSI architecture for RSA public-key cryptosystem is proposed. Due to the simple operation of iterations and the efficient systolic mapping, the proposed architecture computes an n-bit modular exponentiation in n$^{2}$ clock cycles since two modular multiplications for M$_{i}$ and P$_{i}$ in each exponentiation process are interleaved, so that the hardware is fully utilized. We encode the exponent using Radix-4. SD (Signed Digit) number system to reduce the number of modular multiplications for RSA cryptography. Therefore about 20% of NZ (non-zero) digits in the exponent are reduced. Compared to conventional approaches, the proposed architecture shows shorter period to complete the RSA while requiring relatively less hardware resources. The proposed RSA architecture based on the modified Montgomery algorithm has locality, regularity, and scalability suitable for VLSI implementation.

• JSTS:Journal of Semiconductor Technology and Science
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• v.17 no.1
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• pp.101-109
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• 2017

This paper presents a high-throughput low-complexity 512-point eight-parallel mixed-radix multipath delay feedback (MDF) fast Fourier transform (FFT) processor architecture for orthogonal frequency division multiplexing (OFDM) applications. To decrease the number of twiddle factor (TF) multiplications, a mixed-radix $2^4/2^3$ FFT algorithm is adopted. Moreover, a dual-path shared canonical signed digit (CSD) complex constant multiplier using a multi-layer scheme is proposed for reducing the hardware complexity of the TF multiplication. The proposed FFT processor is implemented using TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed FFT processor can lead to a 16% reduction in hardware complexity and higher throughput compared to conventional architectures.

• ETRI Journal
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• v.29 no.3
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• pp.363-370
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• 2007

In this paper, we propose a flexible turbo decoding algorithm for a high order modulation scheme that uses a standard half-rate turbo decoder designed for binary quadrature phase-shift keying (B/QPSK) modulation. A transformation applied to the incoming I-channel and Q-channel symbols allows the use of an off-the-shelf B/QPSK turbo decoder without any modifications. Iterative codes such as turbo codes process the received symbols recursively to improve performance. As the number of iterations increases, the execution time and power consumption also increase. The proposed algorithm reduces the latency and power consumption by combination of the radix-4, dual-path processing, parallel decoding, and early-stop algorithms. We implement the proposed scheme on a field-programmable gate array and compare its decoding speed with that of a conventional decoder. The results show that the proposed flexible decoding algorithm is 6.4 times faster than the conventional scheme.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.3 s.357
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• pp.35-42
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• 2007

The finite-field division can be applied to the elliptic curve cryptosystems. However, an efficient algorithm and the hardware design are required since the finite-field division takes much time to compute. In this paper, we propose a radix-4 systolic divider on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed divide, is mathematically developed and new counter structure is proposed to map on low-cost systolic cells, so that the proposed systolic architecture is suitable for YLSI design. Compared to the bit-parallel, bit-serial and digit-serial dividers, the proposed divider has relatively effective high performance and low cost. We design and synthesis $GF(2^{193})$ finite-field divider using Dongbuanam $0.18{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.3
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• pp.563-569
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• 2007

As the mobile communication and the semiconductor technology is improved continuously, mobile contents such as the multimedia service and the 2D/3D graphics which require high level graphics are serviced recently. Mobile chips should consume small die area and low power. In this paper, we design a truncated floating-point multiplier that is useful for the 2D/3D vector graphics in mobile devices. The truncated multiplier is based on the radix-4 Booth's encoding algorithm and a truncation algorithm is used to achieve small area and low power. The average percent error of the multiplier is as small as 0.00003% and neglectable for mobile applications. The synthesis result using 0.35um CMOS cell library shows that the number of gates for the truncated multiplier is only 33.8 percent of the conventional radix-4 Booth's multiplier.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.10 no.4
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• pp.81-93
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• 2000

In a methodological approach to improve the processing performance of modulo exponentiation which is the primary arithmetic in RSA crypto algorithm, we present a new RSA hardware architecture based on high-radix modulo multiplication and CRT(Chinese Remainder Theorem). By implementing the modulo multiplier using radix-16 arithmetic, we reduced the number of PE(Processing Element)s by quarter comparing to the binary arithmetic scheme. This leads to having the number of clock cycles and the delay of pipelining flip-flops be reduced by quarter respectively. Because the receiver knows p and q, factors of N, it is possible to apply the CRT to the decryption process. To use CRT, we made two s/2-bit multipliers operating in parallel at decryption, which accomplished 4 times faster performance than when not using the CRT. In encryption phase, the two s/2-bit multipliers can be connected to make a s-bit linear multiplier for the s-bit arithmetic operation. We limited the encryption exponent size up to 17-bit to maintain high speed, We implemented a linear array modulo multiplier by projecting horizontally the DG of Montgomery algorithm. The H/W proposed here performs encryption with 15Mbps bit-rate and decryption with 1.22Mbps, when estimated with reference to Samsung 0.5um CMOS Standard Cell Library, which is the fastest among the publications at present.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.11
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• pp.123-130
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• 2004

This paper describes a multiplier architecture optimized for 32 bit RISC processor with 3-stage pipeline. The multiplier of ARM7, the target processor, is variably carried out on the execution stage of pipeline within 7 cycles. The included multiplier employs a modified Booth's algerian to produce 64 bit multiplication and addition product and it has 6 separate instructions. We analyzed several multiplication algorithm such as radix4-32${\times}$8, radix4-32${\times}$16 and radix8-32${\times}$32 to decide which multiplication architecture is most fit for a typical architecture of ARM7. VLSI area, cycle delay time and execution cycle number is the index of an efficient design and the final multiplier was designed on these indexes. To verify the operation of embedded multiplier, it was simulated with various audio algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.1025-1031
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• 2007

This paper proposes an area-efficient pipeline FFT processor for MIMO-OFDM systems with four transmitting and four receiving antennas. Since the MIMO-OFDM system transmits multiple data streams, the complexity for the MIMO-OFDM system with a single-channel FFT processor increases linearly with the increase of the number of transmit channels. The proposed FFT processor is based on multi-channel structure, and therefore it can efficiently support multiple data streams. With the mixed radix algorithm, the number of non-trivial multiplications of the proposed FFT processor is decreased. The proposed FFT processor is synthesized with CMOS $0.18{\mu}m$ process and reduces the logic gates by 25% over a 4-channel Radix-4 multi-path delay commutator (R4MDC) FFT processor. Since the MIMO-OFDM FFT processor is one of the largest modules in the systems, the proposed FFT processor will be a vast contribution improvement to the low complexity design of MIMO-OFDM systems.

• The Transactions of the Korea Information Processing Society
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• v.3 no.4
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• pp.992-1001
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• 1996

Radix sort scans the data twice in a pass, to search bit 0s of the items being sorted and store them into the lowest address, and to search bit 1s and st ore them into the following addresses. This doubles the sorting time. In this paper, we introduce Reverse Radix Sort Algorithm, in which the data being sorted are sacnned just once and write upward from the lowest address if it is 0 and downward from the highest address if it is 1. The algorithm is simple and the hardware sorter implemented by this method shows very high sorting sped. Hardware implementation requires two separate pocket memories, register, an upward increasing address counter, a downward decreasing address counter, and comparator. The software simulation of Reverse Radix Sor Algorithm performs sorting in the speed of 54.9ms per 10 thousand of 8 bit digit data, but the hardware sorter spends 5.3ms to sort the same number of data.